The Power of an Equation

This blog is based on a mathematical equation that took down a multi-billion dollar industry. But fear not, I won’t bore you with the equation. But I still hope to help explain how that equation did that. Sound impossible? But hey, didn’t Richard Feynman introduce his QED theory to the public by saying:

“It is my task to convince you not to turn away because you don’t understand it.”

So, at the risk of sounding (very) arrogant, I’ll attempt what Feynman said.

The equation in question is called the Fourier transform. Jamie Condliffe wrote this awesome article explaining it. His one line non-technical description of it:

“Complicated signals could be represented by simply adding up a series of far simpler ones.”

That’s it. That’s all the maths we need to know for this blog! Really.

That maths is the heart of the MP3 format used for music files in the digital age. Simply put, MP3 applies the Fourier transform on a music file to break the “complicated signal” (aka the song) into “a series of far simpler ones”. It then rejects the “simpler ones” that are at frequencies that we humans can’t hear or can’t really distinguish anyway. The result?

“A file that’s less than a tenth of the size, too.”

Go back to the late 90’s, when the Internet was just picking up. Music was getting digitized by college kids who put the songs on their computers for others to download (for free, aka music piracy). In those days, with low Internet speeds and broadband rare/unheard of, a reduction in file size to “a tenth of the size” made a phenomenal difference to how fast people could download those pirated songs.

Stephen Witt, author of How Music Got Free, tells Mona Lalwani:

“The music industry was [made up of] technophobes. When this information [about the MP3] first became available, they rejected it multiple times. The pirates [started] providing leaked compressed music through the internet and filling a vacuum that the music industry would not. The music corporations could've done that. They ended up being forced to do it much later anyway. But for a long time, they had to be dragged screaming into the modern era.”

As Walter Isaacson narrates it in his biography of Steve Jobs, the message finally got through to the music executives when Jobs told them in his typical style:

“You have your heads up your asses.”

But the damage was already done. As Witt points out:

“Even today they're only operating at about half the size that they were at the peak of compact discs in 2000.”

Of course, while the music industry was overturned, the transition to MP3’s marked the rise of a new giant, Apple. Witt correctly points out:

“Eventually people wanted to take all these files and make them portable. The iPod made that possible. So for a time it became the best-selling gadget ever.”

An entire industry was cut at the knees thanks to the power of an equation; and  the rise of the most valuable company in history (Apple) began with a technology (MP3) built on that equation.